Theorems · Theorem · global analysis

ContDiffBump.hasCompactSupport_normed

∀ {E : Type u_1} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E] [inst_2 : HasContDiffBump E]
  [inst_3 : MeasurableSpace E] {c : E} (f : ContDiffBump c) {μ : MeasureTheory.Measure E} [BorelSpace E]
  [FiniteDimensional ℝ E] [MeasureTheory.IsLocallyFiniteMeasure μ] [μ.IsOpenPosMeasure], HasCompactSupport (f.normed μ)

Defined in: Mathlib.Analysis.Calculus.BumpFunction.Normed
Cited by: 1 results in Mathlib
Foundations: Depth 260 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: NormedAddCommGroup NormedSpace HasContDiffBump MeasurableSpace BorelSpace FiniteDimensional MeasureTheory.IsLocallyFiniteMeasure MeasureTheory.Measure.IsOpenPosMeasure

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Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Realstatement and proof · cited by 25,697
NormedAddCommGroupstatement and proof · cited by 15,752
MeasurableSpacestatement and proof · cited by 13,106
NormedSpacestatement and proof · cited by 12,499
MeasureTheory.Measurestatement and proof · cited by 10,939
FiniteDimensionalstatement and proof · cited by 1,854
BorelSpacestatement and proof · cited by 1,602
IsCompactproof · cited by 1,282
HasCompactSupportstatement · cited by 196
MeasureTheory.IsLocallyFiniteMeasurestatement and proof · cited by 171
MeasureTheory.Measure.IsOpenPosMeasurestatement and proof · cited by 80
ContDiffBumpstatement and proof · cited by 61

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.LocallyIntegrable.exists_contDiff_dist_le_of_forall_mem_ball_dist_leproof · cited by 1